Filling area between two planes in 3d plot

I'm trying to more or less plot an amorphous blob on a 3d plot. I know the top, and I know the bottom. Is there an easy way to fill the space between? For example, if I have

surf(peaks)
hold on
surf(peaks + 5)
hold off

How could I connect the two planes so it's like a volume?

Thank you so much for your time

Answer 1

[Mike Garrity]

The isosurface approach that Tim suggested is possible. Here's an example of how you'd do that. It's a bit involved and it uses quite a bit of memory:

%%Start with 2 surfaces
nx = 25;
ny = 25;
nz = 25;
[x,y] = meshgrid(linspace(-2,2,nx),linspace(-2,2,ny));
z1 = peaks(x,y);
z2 = peaks(x,y) + 5;

surf(x,y,z1);
hold on
surf(x,y,z2)

%%Create 3D grid containing distance to closest surface
[y3,x3,z3] = ndgrid(linspace(-2,2,ny),linspace(-2,2,nx),linspace(-10,15,nz));
v = zeros(size(z3));
for r=1:ny
    for c=1:nx
        for s=1:nz
            d1 = z3(r,c,s) - z1(r,c);
            d2 = z2(r,c) - z3(r,c,s);
            if d1 < 0
                v3(r,c,s) = d1;
            elseif d2 < 0
                v3(r,c,s) = d2;
            else
                v3(r,c,s) = min(d1,d2);
            end
        end
    end
end

%%Create isosurface
figure
p = [patch(isosurface(x3,y3,z3,v3,0)), ...
     patch(isocaps(x3,y3,z3,v3,0))];
isonormals(x3,y3,z3,v3,p(1)) 
set(p,'FaceColor','yellow')
set(p,'EdgeColor','none')
set(p,'FaceLighting','gouraud')
view(3)
camlight right

You need both isosurface and isocaps there. The isosurface command creates the parts inside the volume (the same parts surf created) while isocaps creates the parts along the boundary. You can also combine isocaps from that example with your surface objects like this:

figure
surf(x,y,z1);
hold on
surf(x,y,z2)
isocaps(x3,y3,z3,v3,0);

[Colby]

Thanks a lot!

[Mike Garrity]

If you are going to go the isocaps route, then you're probably going to need to worry about time/memory performance tradeoffs. For example, in some cases it will probably be much better to get rid of those nested for loops and use extra temporary variables instead.

[y3,x3,z3] = ndgrid(linspace(-2,2,ny), ...
                    linspace(-2,2,nx), ...
                    linspace(-10,15,nz));
v3 = min(z3 - repmat(z1,[1 1 nz]), ...
         repmat(z2,[1 1 nz]) - z3);

I think that this would take a lot less time, when you have enough memory for those expanded copies of z1 & z2.

But if you really end up against the performance wall, then Tim Jackman's other suggestion about creating the patches yourself will probably be the way to go.

[Ksenia Shukhin]

Hi Mike!

I have used your code for creation a 3d object, thank you a lot. But now the question is how to create stl file from this. Maybe you can help?

Answer 2

[Tim Jackman]

One option would be to create an isosurface, but to do that you would need to convert your data into a 3-D gridded data. This link has some more information and a couple examples to follow:

http://www.mathworks.com/help/matlab/ref/isosurface.html

Based on the example you provided, and quick way to fill the space in between the two surfaces would be to apply a patch. For example:

surf(peaks)
hold on
surf(peaks + 5)
hold off

Now place a polygon along one edge by supplying the X, Y, and Z coordinates along with the color you want:

patch([1;1;49;49],[1;1;1;1],[0;5;5;0],[1,0,0])

You can get more information on the patch objects here:

http://www.mathworks.com/help/matlab/ref/patch.html